Final answer:
Given the values a=4 and b=6, cell A is 100 times larger than cell B. The larger the cell, the smaller its surface area-to-volume ratio becomes, making exchange processes less efficient compared to smaller cells with higher surface area-to-volume ratios.
Step-by-step explanation:
The diameter of cell A is 2.3 x 10-a, and the diameter of cell B is 2.3 x 10-b. To determine which cell is larger given specific values of a and b, we can substitute the values into the exponents. If a = 4 and b = 6, the diameters become 2.3 x 10-4 for cell A and 2.3 x 10-6 for cell B. To compare the sizes, we divide the diameter of cell A by the diameter of cell B:
(2.3 x 10-4) / (2.3 x 10-6) = 102 = 100.
Therefore, cell A is 100 times greater in diameter than cell B. The correct answer is A.
When considering the efficiency of a cell in exchange of nutrients and wastes, the surface area-to-volume ratio is crucial. A cell with a larger surface area-to-volume ratio will generally exchange substances more efficiently. With their descriptions provided, if cell B has a larger diameter than cell A, then it likely has a smaller surface area-to-volume ratio because as the cell's size increases, this ratio decreases.
If a spherical cell has a diameter of 5 µm, its surface area will be 4πr² and its volume will be (4/3)πr³. A cubed-shaped cell of side length 7μm will have a surface area of 6 × (side length)² and a volume of (side length)³. Calculation of their respective surface area-to-volume ratios will indicate which is more efficient in exchange with its environment.